SUMMARYComputation of a moving interface by the level-set (LS) method typically requires reinitialization of LS function. An inaccurate execution of reinitialization results in incorrect free surface capturing and thus errors such as mass gain/loss so that an accurate and robust reinitialization process in the LS method is essential for the simulation of free surface flows. In the present study, we pursue further development of the reinitialization process, which directly corrects the LS function after advection is carried out by using the normal vector to the interface instead of solving the reinitialization equation of hyperbolic type. The Taylor-Galerkin method is adopted to discretize the advection equation of the LS function and the P1P1 splitting finite element method is applied to solve the Navier-Stokes equation. The proposed algorithm is validated with the well-known benchmark problems, i.e. stretching of a circular fluid element, time-reversed single-vortex, solitary wave propagation, broken dam flow and filling of a container. The simulation results of these flows are in good agreement with previously existing experimental and numerical results.

SUMMARY A Q2Q1 (quadratic velocity/linear pressure) finite element/level‐set method was proposed for simulating incompressible two‐phase flows with surface tension. The Navier–Stokes equations were solved using the Q2Q1 integrated FEM, and the level‐set variable was linearly interpolated using a ‘pseudo’ Q2Q1 finite element when calculating the density and viscosity of a fluid to avoid an unbounded density/viscosity. The advection of the level‐set function was calculated through the Taylor–Galerkin method, and the direct approach method is employed for reinitialization. The proposed method was tested by solving several benchmark problems including rising bubbles exhibiting a large density difference and the surface tension effect. The numerical results of the rising bubbles were compared with the existing results to validate the benchmark quantities such as the centroid, circularity, and rising velocity. Furthermore, we focused our attention mainly on mass conservation and time‐step. We observed that the present method represented a convergence rate between 1.0 and 1.5 orders in terms of mass conservation and provided more stable solutions even when using a larger time‐step than the critical time‐step that was imposed because of the explicit treatment of surface tension. Copyright © 2011 John Wiley & Sons, Ltd.

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